The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  2  8  2  1  2  1  1  0  1  2  8  2  1  4  4  1  2  1  1  1  1  2  1  1  2  1  1  2  1  1  2  1  1  1  1
 0  2  0  2  0  0  6 14  4  4 10  6 12  6 10  4  4 12  2  2  4  8  0  2 12  2  6 14 10  8  0  2 10  8  2  2  4  4  0  0  2 10  0  2 14 12  2  2 14  2  4  4  8  6  4  4  0 10  8  6 14 10  2  2  6 10  2 10
 0  0  2  2 12  6  6  4  4  2  6  0  8 10  4 14  4 10  6 10  6  0 14 12  8  0 12 10  0  2  4  8  2  2 10 10 14 14 10  8  8 14  6  4 10  8  4  2  0 12  0 14 10 14  6 10  6  2  8 12  4  0  6  2 14  4  6 10
 0  0  0  8  0  0  8  0  0  0  8  8  8  0  8  8  8  0  0  0  8  0  8  0  8  8  0  0  0  8  8  8  8  0  0  0  8  8  8  0  8  8  8  8  8  0  0  0  0  8  8  0  0  8  0  8  8  0  8  8  8  0  0  8  8  0  0  0
 0  0  0  0  8  0  8  0  8  8  0  0  0  8  0  0  8  8  0  0  0  0  8  8  8  8  8  8  8  8  0  8  8  8  8  8  8  0  0  8  0  8  8  8  8  0  0  8  0  8  0  0  8  0  0  0  8  0  8  8  0  8  0  0  8  8  8  0
 0  0  0  0  0  8  0  8  8  0  8  0  0  8  8  8  0  8  8  0  0  8  8  8  8  0  0  0  0  0  8  8  8  0  0  8  0  8  0  0  8  8  8  8  0  0  0  8  8  0  8  0  8  8  8  8  0  8  8  0  0  8  0  0  8  0  0  0

generates a code of length 68 over Z16 who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+339x^62+164x^63+609x^64+488x^65+1021x^66+920x^67+1364x^68+900x^69+981x^70+420x^71+373x^72+128x^73+268x^74+32x^75+104x^76+20x^77+40x^78+12x^80+6x^82+1x^90+1x^104

The gray image is a code over GF(2) with n=544, k=13 and d=248.
This code was found by Heurico 1.16 in 14.5 seconds.